Studying systems with hidden attractors is new attractive research direction because of its practical and threoretical importance. A novel system with an exponential nonlinear term, which can exhibit hidden attractors, is proposed in this work. Although new system possesses no equilibrium points, it displays rich dynamical behaviors, like chaos. By calculating Lyapunov exponents and bifurcation diagram, the dynamical behaviors of such system are discovered. Moreover, two important features of a chaotic system, the possibility of synchronization and the feasibility of the theoretical model, are also presented by introducing an adaptive synchronization scheme and designing a digital hardware platform-based emulator.

Hidden attractors in a chaotic system with an exponential nonlinear term

A new 3-D chaotic system with infinitely many equilibria is proposed in this brief. It is exciting that these equilibrium points are located on a rounded square loop. Dynamical properties and the circuit implementation of the system are studied and reported.

A Chaotic System With Equilibria Located on the Rounded Square Loop and Its Circuit Implementation

Memristor and time–delay are potential candidates for constructing new systems with complex dynamics and special features. A novel time–delay system with a presence of memristive device is proposed in this work. It is worth noting that this memristive time–delay system can generate chaotic attractors although it possesses no equilibrium points. In addition, a circuitry implementation of such time–delay system has been introduced to show its feasibility.

A novel memristive time–delay chaotic system without equilibrium points

Chaotic systems without equilibrium points have been investigated and received significant attention recently. In this work, we propose a new three-dimensional fractional-order chaotic system without equilibrium. Dynamics of the fractional-order system are investigated and a circuit implementation of the system by using electronic components is presented. Interestingly, bistable chaotic attractors of such fractional system are discovered. In addition, we are able to control and synchronize the system by using active control and unidirectional coupling.

A simple three-dimensional fractional-order chaotic system without equilibrium: Dynamics, circuitry implementation, chaos control and synchronization

Recent evidence suggests that there exists chaos in a few no-equilibrium systems A chaotic system without equilibrium is proposed and studied in this work It is worth noting that due to the absence of equilibrium, such a system belongs to a class of systems with hidden attractor Dynamics properties and the feasibility of the system are investigated by using numerical simulations and circuit implementation Interestingly, this no-equilibrium system has one variable with the freedom of offset boosting

Dynamics and circuit realization of a no-equilibrium chaotic system with a boostable variable

In this work, we demonstrate the use of a Field Programmable Gate Array (FPGA) as a physical platform for realizing chaotic delay differential equations (DDE). Moreover, using our platform, we also experimentally study the synchronization between two time delayed systems. We illustrate two different experimental approaches – one is hardware co-simulation (using a Digilent Atlys with a Xilinx Spartan-6 FPGA) and the other is analog output (using a Terasic DE2-115 with an Altera Cyclone IV E FPGA).

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Synchronization in coupled Ikeda delay systems: Experimental observations using Field Programmable Gate Arrays

In this paper, we show how chaotic time delay systems can be realized physically using a Field Programmable Gate Array (FPGA) platform.

C. K. Subramaniam

Papers

Synchronization in coupled Ikeda delay systems: Experimental observations using Field Programmable Gate Arrays

Chaotic Time Delay Systems and Field Programmable Gate Array Realization